Showing posts with label guest math education. Show all posts
Showing posts with label guest math education. Show all posts

Wednesday, April 11, 2012

Has constructivism increased special-education enrollment in public schools?

By Nakonia (Niki) Hayes


As a teacher and administrator for 28 years, I rebelled against the disastrous fad of constructivism that began in the 1980’s. While its drumbeaters declared it was a higher form of intellectualism, it didn’t seem all that “intelligent” to me. Frankly, I thought it would help create failures among all groups of students—regular, special, and gifted.

For those who don’t know what “constructivism” is, it is an educational theory that, in practice, looks like this in America’s classrooms:
  • It is students from kindergarten through high school “discovering” their own answers by using manipulatives, working in groups, contriving “real world” problems through “project-based’ activities, moving and talking –a lot, and surviving in a hierarchy of those students who can lead and those who must follow according to their skills.
  • It is lots of colorful, jazzy pictures in books and on classroom walls that show many different ethnic groups, women, with gender-neutral stories, and with child-directed activities that only require teacher “facilitation.” Children rule the day.
  • It is feminized instruction that supports the goal of public education to provide egalitarianism or equity, especially to girls and minorities. That’s the priority placed over building excellence, since excellence smacks of cognitive exceptionalism. That ability is not appreciated nor encouraged where equity is to be the norm in classrooms.
  • It ridicules practice and repetition as “drill and kill” and believes anything that requires memorization is a waste of time that should be used for “creative” thinking.
  • It focuses on process, not results. “Process” is the actual “product” of learning.
  • It believes that if students are having fun, according to perceived “learning styles,” they will like going to school and they will learn the academics they need to prepare for the world of work.
No one will ever be able to determine how many hundreds of thousands of children, who came from dysfunctional, even chaotic, home environments and who entered the constructivist classroom with its lack of boundaries, no right or wrong answers, and the expectation to “discover” their own answers, were shuffled from the “feel-good, tolerant, and fun system” into special education programs. For some strange reason, these kids were declared “discipline” problems. Perhaps if they had been given structure and safety based on routines that established boundaries, along with consistency from adult leaders who taught them about individual responsibility, they would have learned the hidden “rules” of school. What they also deserved was the power that comes from learning proven strategies, true results every time, and a respect for the academic giants who came before them and developed universal lessons from diverse cultures.

Although I had taught journalism, English and art for several years in the 1960’s and 1970’s, I returned to education in the 1980’s as a special education teacher after working 17 years in journalistic fields. I came to realize that half of my students should not have been placed in that program. Those students were there because of cultural deprivation and poor curricula, not because of organically-caused learning disabilities. Then through the 1990’s and until my retirement in 2006, I taught regular (traditional) math in grades six through twelve in mostly high-risk schools, was a middle school and high school counselor, and a K-12 principal in two very different school districts: One was an Indian reservation and the other in Seattle with a predominantly white, upper-middle-class population. No matter what the environment, however, I learned that my special education training was invaluable with all groups of learners.

For example, many exhibited, even if not diagnosed, the characteristics of ADHD, dyslexia, and SLD (specific learning disabilities). My under-performing gifted kids were in a separate category, although some states do put them under “special education.”

ADHD

This condition is apparent from birth and must be seen in at least two different environments, not suddenly after one month in kindergarten or shifts to the new puberty-driven warehouse of education called “middle school.” (A sixth-grade teacher once asked me, “When do we get to call it just ‘bad behavior’?”)

Nonetheless, for those who were diagnosed with ADHD, and those who weren’t but who were as inattentive and wiggly, I used the same techniques:
  • Act, don’t yak. The more you talk to an ADHD student, the more he gets lost. That includes working in group projects.
  • Assign them to men teachers, if possible, because men are usually more goal-driven and less talkative. ADHD students want to know the bottom line.
  • If you want to change behavior, change the academics. Make lessons and teaching structured, short, and frequently rewarded. (Even one sticker works.)
  • Keep wall decorations to a minimum. One big, interesting poster is great for discussion and focus. Forget all the ceiling mobiles, color-drenched walls, etc.
  • Give students permission to move their bodies, whether to lie on the floor, sit on a rotating stool, or stand at a bookcase as they write. The more they are in movement with others, however, they can become agitated as they “lose” their direction and perspective on what’s happening.
  • In essence, be clear, direct, and honest (no phony praise). They’ll love you for it.
Dyslexia

While there are no studies to prove it, many of us in education believe the “whole language” fad of the 1980’s helped exacerbate a learning condition called dyslexia. This is an organic auditory problem where a child cannot hear the correct sounds of letters. Phonemic and spelling books were closeted during the 1980’s because they were considered too mechanical and boring in their purpose. Instead, children were to be exposed to great literature and discuss their own “personal” stories. (This made learning more “relevant” to them.) Somehow, they would absorb the rules of grammar and spelling. Instead, we produced a generation who could not spell, write simple sentences and read. It was like teaching children to play the piano by ear rather than by learning the sounds of the notes and requiring practice to master those sounds. Since students weren’t taught phonics from a good phonemic awareness curriculum, they couldn’t read. They were then labeled “dyslexic” and shuffled to remediation/special education programs.

Most dyslexics, like ADHD students, reveal a high intelligence once they get past their processing “disability.” Interestingly, constructivists claim to focus on “processing.” Yet they have disdain for concrete, precise, and universal strategies that help correct episodic processing deficiencies.

Specific Learning Disabilities

When special education students are included in regular classrooms, they need structure, consistent rules and expectations, a sense of safety given by regular routines, and teacher-directed learning. This is not the atmosphere found in constructivist classrooms. Of course, the dynamics of a carefully selected, mixed-ability classroom can indeed work with an organized and talented teacher. There are such teachers out there for mixed classrooms. Mostly, there are not because there are few “carefully mixed” classes.

Special Note: The move in 1989 by the National Council of Teachers of Mathematics (NCTM) to bring equity to girls and minorities in math classrooms meant a giant move toward feminization of mathematics instruction. This would be a major blow to boys since the majority of special education placement was already for male students, particularly those with ADHD diagnoses. The NCTM president in 1996 explained in a radio interview that girls and minorities couldn’t learn math like “white males.” The 2,000-year-old discipline of mathematics, created by diverse cultures around the world, was now pronounced as destructive to girls and minorities. Its “traditional” approach of linear thinking, practice, and memorization of multiplication tables, was only learnable by white boys (and Asians).

This meant new materials and methods would avoid any “traditional” teaching methods. Basic skills that required memorization (which helps build memory capacity) were also seen as unnecessary because students could use calculators and computers for short-term expediency. The result has been a hatred for math among all “sub-groups” of students, a $4 billion private tutoring industry mostly for math, and an unyielding failure rate of American students entering advanced math and science studies.

Under-Performing Gifted Students

The push for egalitarianism was also designed to ignore exceptional, or gifted, students. The all-inclusive classroom where special ed students were blended with regular and gifted students produced another fad called “differentiated learning.” This is a teacher’s nightmare to plan. It is, therefore, usually an unproductive environment for most students.

In the inclusive classroom, a teacher ends up focusing on the neediest children because that is the goal for egalitarians. The regular and gifted students are considered able to fend for themselves. They aren’t. They lose academic opportunities and growth. And they lose their patience, as most humans do when their needs are continually dismissed or openly ignored. A gifted student will shut down as much as any special ed student because he hasn’t learned basic and general strategies on how to approach a solution. Neither one wants to look dumb. “Better to be thought that way than prove it,” they say.

One of the saddest stories I heard was from Dr. Ruby Payne, who conducts professional development training for teachers who work with students and adults from poverty. She explained that third-grade African American boys who showed signs of giftedness were often labeled “emotionally disturbed” and placed in special education. (ADHD children’s symptoms also mirror those of gifted children.) Part of that problem resulted from not knowing how to measure giftedness outside of scores on math and reading tests. Another part was in seeing giftedness as exceptionalism and that was to be downplayed. These children then became under-performing or major disciplinary problems as their own needs, often ones that saw them wanting to work alone, weren’t met in the highly interactive, noisy, motion-filled classrooms designed, teachers thought, to meet lower-performing students’ needs (girls and minorities, except Asians).

Summary

For almost three decades, I personally saw that when children were given explicit, step-driven instruction with consistent consequences of positive results, along with direct teacher support, they learned their required academics no matter what their gender, race, economic status, or intelligence level. This methodology has now been proven according to an article published this month in the American Federation of Teachers’ magazine, American Educator ( http://www.aft.org/pdfs/americaneducator/spring2012/Clark.pdf ).

I therefore believe the radical and destructive implementation of constructivist ideology in education has increased the numbers of students in public schools being labeled “special education” or in the development of characteristics of special needs students.

It is unlikely that anyone can ever tally the unbelievable human and financial costs of education fads in America, with constructivism being the Big Daddy of them all. Education decision-makers grabbed onto unproven and unproductive methods with which they trained and evaluated teachers. Government entities like the National Science Foundation and U.S. Department of Education pumped almost $100 million into the new, unproven curricula and training materials in the 1990’s alone. Private businesses and more non-state government groups are now getting into the picture. Billions of dollars are at stake today, yet no one acknowledges the importance of weak and incoherent curricula on teacher training. Meanwhile, the same members of the leadership circle that have brought American students to their knees are still in charge. The question is “Why?”

Since removal of those leaders seems impossible, local districts can at least offer parents a choice within each school: Do they want their child to follow traditional, explicit curricula or that of the constructivist/reform model? Just once, it would be great to hear an honest answer as to why this can’t be done. And it’s not about money.


Nakonia (Niki) Hayes is the author of "John Saxon's Story: A genius of common sense in math education." She is certified and experienced in journalism, counseling, special education, mathematics, and administration during 28 years in public education. She worked in various journalism fields for 17 years, including with two state senators and a U.S. congressman. She also published historical and contemporary articles on American Indians and Micronesia (with the U.S. Department of Interior) during that period. She is director of K-8 Emmanuel Academy for tutoring of reading, writing, and math in Waco, TX, and she tutors in Saxon Math at a local Catholic elementary school. She has a Web site at this address. Email Niki at nakonia69@saxonmathwarrior.com

This article was previously published on Education Views at: http://educationviews.org/2012/04/10/has-constructivism-increased-special-education-enrollment-in-public-schools/. It was republished here with permission of the author. 



Note from Laurie Rogers: If you would like to submit a guest column on public education, please write to me at
wlroge@comcast.net . Please limit columns to about 1,000 words, give or take a few. Columns might be edited for length, content or grammar. You may remain anonymous to the public, however I must know who you are. All decisions on guest columns are the sole right and responsibility of Laurie Rogers.

Sunday, April 1, 2012

A statistician’s view of constructivist math programs

By Nicole O. Stouffer

"It's like these administrators never even met a child."
- Nik Stouffer

I’ve had 4 years of undergraduate math courses, two years of graduate math courses, and I have taught graduate-level math courses. I had never seen the "lattice" method, the Egyptian method, or any of these other alternative algorithms until last year when I looked at Everyday Math homework. Students don’t need them, and those methods will not help a student move onto higher mathematics.

I would have been laughed out of my college classes if I used the "partial sums" method to add. I wouldn’t have been able to take differential equations if I hadn’t mastered long division. There is a reason why traditional algorithms (the math methods you learned in school to add, subtract, multiply and divide) are needed. Traditional algorithms are needed to understand higher mathematics in college. It is extremely important that they are practiced until they are mastered. In fact, the new Common Core State math standards recommend teaching the standard algorithms.

You might think there is no reason not to offer alternative algorithms, as long as they also teach the traditional methods, but I have three reasons why the teaching of alternative programs is a problem.
  • It is a waste of classroom time. There are plenty of other items to be covered and practiced, so students should avoid learning inefficient algorithms.
  • Offering children too many algorithm choices is confusing. I have seen kids straddle two methods, not really understanding either of them and becoming frustrated.
  • Students are not permitted to use these alternative algorithms in college-level math.
Everyday Math does not prepare students for middle school math. There is a huge disconnect between Everyday Math and the rest of your child’s academic career.

My advice to parents… Work with your child to reinforce the traditional math algorithms that you learned. E-mail your principal and board directors to urge them to stop the use of these alternative methods in school and start using a more traditional textbook that uses the most efficient algorithms recommended by the Common Core State Standards.

Spiraling

The core principle behind Medford’s K-5 math program, Everyday Math, is based on a style called “spiraling,” where students continually return to basic ideas as new concepts are added over the entire year. Mostly, spiraling makes sense because kids need to return to topics periodically throughout the school year to remind them of what they have previously learned so they can build on it.

Everyday Math and other reform math programs like it do not use spiraling in this way. They don’t allow time for a child to master a skill before moving onto something else. The topics change so rapidly that kids never get a chance to feel successful in mathematics. Just as they are working toward figuring a concept out, Everyday Math will abruptly move onto another concept completely unrelated to the last. By the time a student returns (spirals back) to a concept, the child has forgotten the skill. Mathematics is a subject better suited toward mastery because the nature of math itself is linear and builds upon skills that are mastered in a sequential and logical fashion.

Everyday Math, Investigations in Number, Data, and Space, and other reform math programs have been highly criticized because of the lack of “focus” that comes with incoherent topic changes from excessive spiraling. In fact, the Common Core State Standards insist that a math curriculum be “more focused.” The final report of the 2008 President’s National Mathematics Advisory Panel (NMAP) recommends, “A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided."

Of course, the authors of Everyday Math sent a letter arguing, “the spiral approach should be more effective than a focused approach.” They are right, it “SHOULD be,” but it isn’t because of the way they do it. This is the reason the NMAP recommended it should be avoided. The authors of Everyday Math decided that they were right and everyone else was wrong. So Everyday Math still continues to randomly bounce from topic to topic each week and never allow enough time for practice or mastery. Even though the authors refused to change Everyday Math to be more focused, that didn’t stop them from slapping a label on their book that says “Common Core State Standards 100% Alignment.”

Shouldn’t our students have a focused textbook that actually aligns to the more-efficient methods recommended by the President’s National Mathematics Advisory Panel and the Common Core State Standards?

Supplementation

Everyday Math and other reform math programs require a lot of patching and fixing. I have talked with several teachers who have to rip pages out of the book and completely re-order the lessons and add additional lessons to make Everyday Math work. They have to practically rewrite an entire curriculum because Everyday Math is so poorly designed. After a few years, teachers can work out the bugs and the kinks and realize what to throw away and what to add, but if they move to a different grade level then they have to do this work all over again. It’s is a real problem when substitutes or new teachers have to experience this inadequate program for the first time because they might not realize how bad this program really is until they actually start using it to teach.

Last year, I had an issue with statistics because Everyday Math has watered down the First Grade lessons in probability to the point where they’re actually wrong. As a statistician, I find it frustrating to see statistical words used incorrectly and statistical concepts presented incorrectly. I wrote to my child’s teacher, who referred me to the principal. He told me that the teachers were required to teach to the curriculum and there was nothing that could be done about the fact that the book was teaching something incorrectly. The principal suggested that I “write the authors of the book.” I’ve been told by the Board of Education not to worry about the bad math program because teachers supplement to make it work. But how much can teachers really supplement and change from the set curriculum? And why would we insist on giving them such a bad tool that requires so much work on their part? Why don’t we give the teachers the best tools to teach our kids?

Minimally Guided Instruction

You could tell your children to “Go clean your room,” or you can tell them, “Put your dirty clothes in the hamper, make your bed, and put your toys in the toy box and books on your book shelf.” Which of the two examples would teach your children how to clean their room? The first is an example of minimally guided instruction and the second is an example of guidance-specific instruction.

There might be examples where minimally guided instruction is an effective teaching tool, but learning how to clean your room and learning grade-school mathematics aren’t two of them. Unfortunately, the math programs Investigations in Number, Data, and Space, Everyday Math and Connected Mathematics, expect children to ‘discover’ mathematics on their own with minimal guidance from the teacher. Many elementary school teachers in NJ don’t buy into that nonsense, so they provide the little kids with more guidance. In middle school, in some districts in New Jersey, such as Medford township, offer a pre-math class where the student is taught directly, with worked examples, before they get to the actual math class where the student is expected to ‘discover’ math for him/herself. Does that make sense to you? Me neither. Why wouldn’t the school just use a math book that directly teaches math instead of offering two math classes to cover up an ineffective Connected Mathematics book that uses the failed method of minimally guided instruction?

Don’t take my word for it, Kirschner, Sweller, & Clark (2006) show that minimally guided instruction goes against more than fifty years of research on human cognitive architecture. There is overwhelming evidence that minimally guided instruction is a less efficient and less effective teaching style.

A bigger problem that affects all students is that it takes time for a child to ‘discover’ mathematics, so Connected Mathematics wastes a lot of classroom time ‘discovering,’ instead of directly teaching efficient methods for solving math problems. Compared to other middle school math books, Connected Mathematics actually covers less material. This means that all students, especially the kids who don’t need the pre-math class, could be learning more than what is presented in class.

Unfortunately, the missing concepts will eventually catch up with a student when they enter high school algebra because you can’t learn what is never taught.

Nik Stouffer is a statistical consultant with more than 15 years of experience. She has a Masters degree in mathematics and has taught graduate school mathematics classes. Website: http://www.medical-research-support.com/



Note from Laurie Rogers: If you would like to submit a guest column on public education, please write to me at wlroge@comcast.net . Please limit columns to about 1,000 words, give or take a few. Columns might be edited for length, content or grammar. You may remain anonymous to the public, however I must know who you are. All decisions on guest columns are the sole right and responsibility of Laurie Rogers.

Monday, January 3, 2011

"What I see" - Parent volunteer tells heartbreaking tale

By Breann Treffry, school volunteer and parent of three, Spokane, WA


We’ve heard much recently about the United States slipping in the education ranking of developed nations. Having been a product of the American public school system, I knew, like many other American parents, that the education it provides is, shall we say, lacking in certain areas. What I didn’t realize - until I enrolled my own children, immersed myself in their schools, classrooms, curricula, and classmates, attended school board meetings, and heard the stories of other concerned parents and teachers - is just how lacking that education truly is.

From home, it can be hard for parents to understand the damage that’s being done to our kids until it’s too late and our children suddenly require remediation, tutoring, or have their hopes for their future crushed when they discover they’re woefully unprepared for college. When I initially began volunteering at my kids’ school, I admit, it was to monitor the education my own kids were receiving. In these last years, however, the education all our kids are receiving has revealed itself as the train wreck from which I can’t look away. Moral duty compels me to share what I have seen that every parent should know.

While I have either personally witnessed or have reliable sources who have witnessed these atrocities within Spokane Public Schools, they are in no way isolated to this little town in eastern Washington. The trend is nationwide.

  1. Cursive writing is no longer taught.
  2. I see high schoolers who cannot read cursive because they were never taught to write in cursive.
  3. I see math curricula that do not teach standard algorithms, but rather create dependency on calculators and technology.
  4. I see curricula that drive a wedge between students and their parents by fostering a dependency on peers through excessive group work.
  5. I see math curricula that prevent parental involvement by excluding the methods we were taught and teaching only “new math.”
  6. I know parents who can’t help their elementary age children with math homework because it doesn’t make sense to parents or students.
  7. I’ve seen the light come on for students who have struggled for years - after their tutors or parents show them standard algorithms.
  8. I have heard teachers ask parents to “please, please” not teach their children standard algorithms.
  9. I know teachers who have offered classes for parents on how to understand the “new math.”
  10. I know kids who “get in trouble” in class when they use the algorithms they learned at home.
  11. I’ve heard parents and teachers remark that math has “changed so much” since we learned it; but, of course, math doesn’t change. Two plus two still equals four.
  12. I see 12-year-olds who cannot add or subtract, let alone multiply or divide, yet have been pushed through to the next grade regardless.
  13. I’ve heard teachers telling students, “You have to draw pictures to show your work” in math.
  14. I see third and fourth graders who draw literally hundreds of marks or pictures to figure a single math problem because they haven’t been taught efficient methods, and still get the answer wrong.
  15. I’ve seen eleventh graders who cannot divide a 3-digit number by a 1-digit number without a calculator.
  16. I see elementary school classrooms with a calculator in every desk.
  17. I know teachers who have been told not to try to engage struggling and difficult students in lessons but to let them be content with picture books in class.
  18. I know teachers who have been reprimanded for criticizing district curricula or policy.
  19. I see teachers paranoid and intimidated over teaching traditional math like standard algorithms and facts drill in their classrooms.
  20. I’ve heard district administrators openly discussing “problem teachers.”
  21. I see students in classrooms where the teacher taught algorithms and drilled math facts excel the following year over students from classrooms where the teacher did not.
  22. I know volunteer tutors who’ve been refused because they teach traditional math methods rather than “fuzzy” math.
  23. I see students who are “good at math” in tears over their math homework.
  24. I’ve heard a teacher tell students, “Abraham Lincoln fought and died in the Civil War.”
  25. I see an appalling rate of high school graduates who require remedial math courses in college.
  26. I’ve seen students who successfully test into college-level math ultimately struggle and learn that they need remediation after all to fill in the holes in their math education.
  27. I see kids being taught daily to a level far beneath their capacity, and being told that they just have to sit there.
  28. Alternately, I see teachers struggle to provide additional challenges for those kids using only “district-approved curricula.”
  29. I see third graders singing preschool songs as a class.
  30. I’ve seen district-provided material that tells teachers to spend more individual instructional time with lower-performing students than with higher-performing students.
  31. I see students who mock and taunt adults in the school, with no significant consequences.
  32. I see students with multiple truancies that result in no consequences.
  33. I see unexcused absences that go undisciplined.
  34. I see late work given full credit.
  35. I see students receive extra credit points through no effort of their own, for example, when the teacher calls them by the wrong name in class.
  36. I’ve seen implementation of a grading system where it’s often impossible to achieve either the highest or the lowest grade.
  37. I’ve seen materials that tell teachers to train students not to question teachers or other students, not to raise their hand when they have the right answer, and not to take the lead in groups.
  38. I see academic learning time used for social exercises designed to make sure everyone a) feels good and b) realizes that they’re a small part of a large group.
  39. I’ve learned that - despite what the district has claimed - the WASL (now the MSP or HSPE at the high school level) is not required, not at any grade level and not for graduation in the state of Washington – rather, there are several ways to meet the graduation requirement.
  40. I see students’ love of and excitement for learning turning to drudgery and perceived failure.
As much I want to spare my own children from these wrongs, it’s just as wrong for adults to sit quietly by as the next generation, with eyes wide and full of hope and excitement, receives what has become the empty promise of an American public education. The essence of public schools is education for all, yet our schools are falling far short of the claim that they will prepare students to compete as adults, let alone in a global market.

I ask parents and teachers, what have you seen that just doesn’t sit right with you? What have you been told to teach or not to teach? What have your kids brought home that didn’t make sense, but you feel you can only assume that the schools must know best? Any one of these seemingly little things as an isolated incident might not mean much but for our children’s sake, do not discount it. These incidents add up to one giant failure across the country, putting the United States at the bottom of the list. http://www.geographic.org/country_ranks/educational_score_performance_country_ranks_2009_oecd.html#maths

Parents and teachers, you are not alone. Get together, talk, stand up for our children. It’s their future and our nation’s future that are at stake.


This article also was posted Jan. 5, 2011, on EducationNews.org at: http://www.educationnews.org/commentaries/105500.html



Note from Laurie Rogers: If you would like to submit a guest column on public education, please write to me at wlroge@comcast.net. Please limit columns to not more than 1,000 words. Columns might be edited for length, content or grammar. You may remain anonymous to the public, however I must know who you are. All decisions on guest columns are the sole right and responsibility of Laurie Rogers.